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YES

Throughout the ages of biblical times, the saints have declared with trumpets the Justice of God.

Job 34:12 NIV

It is unthinkable that God would do wrong, that the Almighty would
pervert justice.

Deuteronomy 32:4

He is the Rock, his works are perfect, and all his ways are just. A
faithful God who does no wrong, upright and just is he.

2 Thessalonians 1:6

God is just: He will pay back trouble to those who trouble you

Isaiah 30:18

Yet the LORD longs to be gracious to you; therefore he will rise up to
show you compassion. For the LORD is a God of justice. Blessed are all
who wait for him!

Isaiah 5:16

But the LORD Almighty will be exalted by his justice, and the holy God
will be proved holy by his righteous acts.

Why isn't God doing anything about the evil?

You may then ask, why is there evil in this world? Why are there murders and why are there evil people?

God declares that He will judge every deed.

Ecclesiastes 3:17

I said to myself, “God will bring into judgment both the righteous and
the wicked, for there will be a time for every activity, a time to
judge every deed.”

Revelation 20:13

The sea gave up the dead that were in it, and death and Hades gave up
the dead that were in them, and each person was judged according to
what they had done.

How can God forgive us, if He is Just?

God has declared all people wicked, so how can He forgive anybody?

Romans 3:23 (NIV)

for all have sinned and fall short of the glory of God

Well.. isn't that what this entire story is about.

Romans 3:25-26 (NIV)

25 God presented Christ as a sacrifice of atonement, through the
shedding of his blood—to be received by faith. He did this to
demonstrate his righteousness, because in his forbearance he had left
the sins committed beforehand unpunished— 26 he did it to demonstrate
his righteousness at the present time, so as to be just and the one
who justifies those who have faith in Jesus.

Just a thought: personally, I think I prefer the existing answers that focus on justice (re scripture); simply for the reason that for this answer you need to also demonstrate (through scripture) that "perfection" implies "just".
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Marc Gravell♦Jan 4 '12 at 9:26

point taken, however, perfection means being complete by any definition. A perfect body for example can't have missing limbs. So how could God be perfect if he lacked justice?
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LanceJan 4 '12 at 22:48

but you are using an implicit definition that a body includes limbs, based on anatomical familiarity. All I'm saying is that a scriptural reference that "perfection includes justice" would go a long way to making this a better answer. "Complete" could be said to include anything.
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Marc Gravell♦Jan 4 '12 at 22:57

So God is the ultimate reference and authority for everything. He created the world with his standards. He is justice himself.

In this perspective, God not being just is illogical, because it would require an higher authority under which God could be found "wrong".

God could only be felt "injust" by creatures standards, which are automatically inferior to God justice (and thus flawed).

A comparison would be when you (rightfully) punish a child and he says "that's not just". People who dealt with children know what I mean ;)

Addition : a false representation of God could be found injust. The true justice is said to be seeded in every man's soul by God. Against this higher, truer sense of justice coming from God himself, a false representation of God could be rightfully found injust. This should stimulate a real truth seeker to "clean" his representation of God.

Not all Christians believe that. Many Christians--myself included--believe that belief in a god is in fact incompatible with Christianity. You should make sure to explain that your answer is given from a specific Christian perspective (an overwhelming majority perspective, no doubt, but definitely a universal one) and does not claim to speak for all of Christianity.
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Steely DanJan 4 '12 at 17:35

Thou shalt not bow down thyself to them, nor serve them: for I the
LORD thy God am a jealous God, visiting the iniquity of the fathers
upon the children unto the third and fourth generation of them that
hate me; And shewing mercy unto thousands of them that love me, and
keep my commandments. (Exodus 20:5-6)